MATLAB: Simultaneous parabolic PDEs: pdepe error “Attempted to access u(4); index out of bounds because numel(u)=1.”

pdepdepesimultaneous pdes

Hi all, I have never done this before, so pardon my formatting. I have a fairly long PDE solver function written, and I have attached it so as to save space. The abridged version of the problem I am having is in the pdefun subfunction of the solver. when the program reaches the first line under "%Concentration reactions," I receive the error "Attempted to access u(4); index out of bounds because numel(u)=1." There is probably a simple explanation that I am just missing. any help would be great, Thanks
function [c,f,s] = pdefun(x,t,u,DuDx)
%diffusion constants:
DCO2 = 2*10^-9;        %all in m^2 s^-1
DHCO3 = 1.18*10^-9;
DCO3 = .995*10^-9;
DH = 9.31*10^-9;
DOH = 5.27*10^-9;
DBOH3 = 1.11*10^-9;
DBOH4 = .97*10^-9;
%diffusion matrix:
Ds=[DCO2 DHCO3 DCO3 DH DOH DBOH3 DBOH4];
T = 298.15;     %seawater temp, degrees K
S = 35;      %seawater salinity
%General Calculated Constants:
K_1 = exp(2.83655-2307.1266/T-1.5529413*log(T) ...
      +(-0.20760841-4.0484/T)*S^0.5+0.0846834*S-0.00654208*S^1.5);                                  % Roy 1993
K_2 = exp(-9.226508-3351.6106/T-0.2005743*log(T) ...
      +(-0.106901733-23.9722/T)*S^0.5+0.1130822*S-0.00846934*S^1.5);             
K_w = exp(-13847.26/T+148.9652-23.6521*log(T) ...
      +(118.67/T-5.977+1.0495*log(T))*S^0.5-0.01615*S);                                             % DOE 1994

K_B = exp((-8966.90-2890.53*S^.5-77.942*S+1.728*S^1.5-0.0996*S^2)/T ...
      +148.0248+137.1942*S^.5+1.62142*S -(24.4344+25.085*S^.5+0.2474*S)*log(T)+0.053105*(S^.5)*T);  % DOE 1994
%Carbonate Chemistry Reaction Constants:  
kp1 = exp(1246.98-6.19e4/T-183.0*log(T));             % Schulz et al. 2006










km1 = kp1/K_1;                                        % Schulz et al. 2006
A_4 = 499002.24*exp(4.2986e-4*S^2+5.75499e-5*S);      % Schulz et al. 2006
kp4 = A_4*exp(-90166.83/8.31451/T)/K_w;               % Schulz et al. 2006
km4 = kp4*K_w/K_1;                                    % Schulz et al. 2006
kp5H = 5.0e10;                                        % Schulz et al. 2006
km5H = kp5H*K_2;                                      % Schulz et al. 2006
kp5OH = 6.0e9;                                        % Schulz et al. 2006
km5OH = kp5OH*K_w/K_2;                                % Schulz et al. 2006
kp6 = 1.40e-3;                                        % Schulz et al. 2006
km6 = kp6/K_w;                                        % Schulz et al. 2006
km7 = 10^10;
kp7 = 20;
%concentration reactions:
CO2  = ((km1*u(4) + km4)*u(2) - (kp1 + kp4*u(5))*u(1))/Ds(1,1);
HCO3 = (kp1*u(1) - km1*u(4)*u(2) + kp4*u(1)*u(5) - km4*u(2) + kp5H*u(4)*u(3) - km5H*u(2) + km5OH*u(3) - kp5OH*u(5)*u(2))/Ds(2,1);
CO3  = (km5H*u(2) - kp5H*u(4)*u(3)+ kp5OH*u(5)*u(2) - km5OH*u(3))/Ds(3,1);
H    = ((km5H - km1*u(4))*u(2) + kp1*u(1) - kp5H*u(4)*u(3) + kp6 + km6*u(5)*u(4) + kp7*u(6) - km7*u(4)*u(7))/Ds(4,1);
OH   = (km4*u(2) - kp4*u(1)*u(5) -kp5OH*u(5)*u(2)+km5OH*u(3) + kp6 + km6*u(4)*u(5))/Ds(5,1);
BOH3 = (-kp7*u(6) + km7*u(4)*u(7))/Ds(6,1);
BOH4 = (kp7*u(6) - km7*u(4)*u(7))/Ds(7,1);
%Set PDE Values
c=ones(1,7)/Ds;
f=ones(1,7) .*DuDx;
s=[CO2; HCO3; CO3; H; OH; BOH3; BOH4];

Best Answer

Hi Nathaniel,
The error you encountered is because 'pdepe' is making a function call to 'pdex1ic' and 'pdex1bc' which are different from your initial conditions and boundary conditions function. The function call in 'pdepe' needs to be as follows:
sol = pdepe(m,@pdefun,@icfun,@pcfun,xmesh,tspan);
That will resolve the error you encountered. However, there are a few other issues within your code:
  1. You assume that local functions (such as 'pdex1ic' and 'pdex1bc') have access to the variables defined in other functions in your code. This is not true. Every local function has its own workspace. Please refer to the following link for information on base and function workspace.
  2. As mentioned in the earlier comment, you need to make sure 'c' and 'f' are column vectors.
I hope that helps.
Ghada
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